The most common and most likely answer to this crossword clue is the 10 letter word RADICALISE
R
A
D
I
C
A
L
I
S
E
More clues leading to the result RADICALISE
Buddy explains!

The straight part
We know that "Make extreme" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case make extreme = radicalise.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does RADICALISE mean?
RADICALISE verb- To make radical.
- To become radical; to adopt a radical political stance.